Horosphere is surface in hyperbolic space that is isometric to the Euclidean plane. In order to correctly visualize hyperbolic space we embed flat computer screen as horosphere and investigate geometry of central projection of hyperbolic space onto horosphere. We also discuss realization of hyperbolic isometries. Corresponding algorithms are implemented in Mathematica package L3toHorospere. We ...

We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We show that critical points of the generalized volume are associated to geometric structures modeled on the extended hyperbolic space – the natural extension o...

We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility t...